Bedtime stories

From RP:

In response to your request for stories …

I well remember at the age of 8 or maybe just 9, lying awake in bed trying to find a mixed number that when multiplied by itself gave an answer of exactly 2.
I was trying number like “one and a half” and “one and a quarter” and finding that when I multiplied them by themselves the bottom line always got unhelpfully large.

I think I was just coming to the conclusion that it couldn’t be done when I fell asleep.